The problem of determining whether a given system is locally controllable and/or locally stabilisable is difficult. In this talk, an approach for characterising the geometric structure of these problems will be outlined. Specifically, the problems will be reduced to questions involving affine subbundles. Once this reduction is accomplished, some existing results in controllability and stabilisation, probably familiar to most, will be expressed in this geometric language, as a warmup. Then some not so well-known (i.e., new) results will be given. The idea will be to illustrate some apparent (but not proved) connections between controllability from a point and stabilisability to a point.
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